Minor losses in pipe flow

Minor losses in pipe flow are a major part in calculating the flow, pressure, or energy reduction in piping systems. Liquid moving through pipes carries momentum and energy due to the forces acting upon it such as pressure and gravity. Just as certain aspects of the system can increase the fluids energy, there are components of the system that act against the fluid and reduce its energy, velocity, or momentum. Friction and minor losses in pipes are major contributing factors.[1][2][3][4]

Minor Losses

Below is a list of common piping components and their kinetic energy factor, ${\displaystyle e_{v}}$.

Kinetic energy factors for specific components of piping systems. Provided by John Berg, Chemical Engineering, University of Washington.

The kinetic energy factor is used to calculate the configurational head loss, the energy loss to the components of the system. The configurational head loss, ${\displaystyle H_{Lc}}$, can be calculated using the following equation.

${\displaystyle H_{Lc}={v^{2} \over 2g}(\sum _{i}e_{v,i})}$[5][2][6]

Where:

${\displaystyle H_{Lc}}$= Configurational head loss

${\displaystyle v}$= Downstream velocity

${\displaystyle g}$= Gravity of Earth

${\displaystyle \sum _{i}e_{v,i}}$= Sum of all kinetic energy factors in system

Friction Losses

Before being able to use the minor head losses in an equation, the losses in the system due to friction must also be calculated.

Equation for friction losses:

${\displaystyle H_{Lf}={v^{2} \over gR_{h}}(\sum _{i}L_{i})f}$[5][3][1]

${\displaystyle H_{Lf}}$= Frictional head loss

${\displaystyle v}$= Downstream velocity

${\displaystyle g}$ = Gravity of Earth

${\displaystyle R_{h}}$ = Hydraulic radius

${\displaystyle \sum _{i}L_{i}}$ =Total length of piping

${\displaystyle f}$ = Fanning friction factor

Total Head Loss

After both minor losses and friction losses have been calculated, these values can be summed to find the total head loss.

Equation for total head loss, ${\displaystyle H_{L}}$, can be simplified and rewritten as:

${\displaystyle H_{L}={v^{2} \over 2gR_{h}}[(2\sum _{i}L_{i})f+R_{h}(\sum _{i}e_{v,i})]}$[5]

${\displaystyle H_{L}}$= Frictional head loss

${\displaystyle v}$= Downstream velocity

${\displaystyle g}$ = Gravity of Earth

${\displaystyle R_{h}}$ = Hydraulic radius

${\displaystyle \sum _{i}L_{i}}$ =Total length of piping

${\displaystyle f}$ = Fanning friction factor

${\displaystyle \sum _{i}e_{v,i}}$= Sum of all kinetic energy factors in system

Once calculated, the total head loss can be used to solve the Bernoulli Equation and find unknown values of the system.[1][5]

See also

• Hydraulic head
• Total dynamic head

Notes

1. "Losses in Pipes". my.me.queensu.ca. Retrieved 23 January 2017.
2. Anderson, Gunther; Ryan Barr; Risa Benvega. "Minor Losses" (PDF). Retrieved 23 January 2017.
3. "Head Loss in Piping Systems - TechInfo". www.hydromatic.com. Retrieved 2017-01-22.
4. "Objectives_template". nptel.ac.in. Retrieved 23 January 2017.
5. Lightfoot, R. Byron Bird; Warren Stewart; Edwin N. (2007). Transport phenomena (Rev. 2. ed.). New York [u.a.]: Wiley. ISBN 978-0-470-11539-8.
6. "Minor Loss Calculation for Liquid and Gas Flow". www.lmnoeng.com. Retrieved 2017-01-22.